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The modified model of radar images


A.V. Korennoy – Honored Scientist of RF, Dr. Sc. (Eng.), Professor of Department, MESC «Zhukovsky–Gagarin Air Force Academy» (Voronezh)
S.A. Lepeshkin – Ph. D. (Eng.), Deputy Head of Department № 95, Mozhaysky Military Space Academy (Saint Petersburg)
E.A. Yashchenko – Post-graduate Student of Department № 122, MESC «Zhukovsky–Gagarin Air Force Academy» (Voronezh)
O.A. Mishukov – Post-graduate Student of Department № 95, Mozhaysky Military Space Academy (Saint Petersburg)

Today, a rapid development of the radio electronics, component base, and signals operation modes allows creating high-efficiency com-plexes of the surface remote sounding independent from the weather and time of day. One of the promising directions in this field is re-mote sounding of the surface with the use of the radar locator with synthesized aperture antenna (RSA) that allows forming highly de-tailed radio location images (RLI). The RSA formed radar location image is influenced by a number of destructive factors such as external additive disturbance, trajectory instability when determining image generating characteristics, speckle noise and others. As far as the problem of RLI restoration is an incorrect problem, it is needed a priori information about a generated RLI for its solution. One of the re-quired parameters for optimal image restoration by means of the statistical regularization method based on Bayesian approach is a priori correlation function of the generated RLI that is presented as a space function. The RLI mathematical model is posed by means of linear stochastic differential equations in second-order partial derivatives. These equations determine directly the process of generation for a collection of an image as well as allow analyzing probabilistic characteristics of the resulting models.
Real RLIs have a set of features determined by a specific character of electromagnetic waves diffraction of the radiofrequency range on the surface of shaped form artificial objects, and it is necessary to take into account these features when choosing the mathematical model. The analysis of RLI peculiarities allowed to develop modified mathematical models of real RLIs by means of differentiation of the initial models according to their space coordinates on the basis of stochastic differential equations in second-order partial derivatives. The result is the correlation functions of the modified models.
It was made a comparison between mathematical models correlation functions and real RLIs statistical correlation functions in order to assess the adequacy of the mathematical models to the real RLI. The analysis was performed with the use of the concrete model of the initial image presented as a linear differential parabolic equation. The problem was solved by means of a least-square method with condition for minimum of the error mean square for various parameter points of the models. Considering great RLI dependence from the frequency range, it was made an analysis for the adequacy of the models for various RSA frequency ranges. The results demonstrated that the mathematical model presented as a mixed derivative of the parabolic model has the best correlation characteristics for describing real RLIs of various ranges from 1 centimetre to 1 metre. The mathematical model presented as a combined derivative is good for describing RLIs within long-wave ranges (L and P) but the error value increases for centimetre ranges.

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